Problem 2 (20 points). A university endowment fund is a collection of donations of money or property to the university. Universities invest this money per directed by donors or as they see fit. More information on what endowments are and what they do can be found here: https://www.investopedia.com/ask/answers/how-do-university-en Below is a subset of Midwestern universities and their endowment funds for fiscal year 2018: Endowment FY2018 (millions of dollars) Institution University of Michigan Northwestern University University of Chicago Ohio State University University of Minnesota University of Wisconsin foundation Michigan State University University of Iowa University of Cincinnati Iowa State University Oklahoma State University Medical College of Wisconsin Oberlin College Marquette University Loyola University of Chicago University of Wyoming Kansas State University Illinois Institute of Technology Hope College Rockhurst University University of Detroit Mercy 11901.76 11087.459 7928.485 5211.434 3717.476 2985.251 2907.767 1500.546 1367.426 1063.772 983.881 930.961 905.947 668.567 643.806 513.201 480.375 235.271 225.656 33.199 58.674 (a) Calculate the five-number summary for this data set, and give a boxplot. Comment on observations. (b) Find the 6oth percentile of this dataset. /5
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Can you do Problem 2 questions (a) and (b)?
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